copyright © 2011 pearson education, inc. samples and surveys chapter 13
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13.1 Two Surprising Properties of Sampling
How is the winning car model of J.D. Power and Associates Initial Quality Award determined?
By focusing on a subset of the whole group (a sample)
By making sure that items are selected randomly from the larger group
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13.1 Two Surprising Properties of Sampling
Definitions
Population: the entire collection of interest Sample: subset of the population Survey: posing questions to a sample to learn
about the population Representative: samples that reflect the mix in
the entire population Bias: systematic error in selecting the sample
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13.1 Two Surprising Properties of Sampling
The two surprises are:
The best way to get a representative sample is to pick members of the population at random.
Larger populations do not require larger samples.
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13.1 Two Surprising Properties of Sampling
Randomization
A randomly selected sample is representative of the whole population.
Randomization ensures that on average a sample mimics the population.
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13.1 Two Surprising Properties of Sampling
Comparison of Two Random Samples from a Population of 3.5 Million Customers.
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13.1 Two Surprising Properties of Sampling
Randomization
Produces samples whose averages resemble those in the population (avoids bias).
Enables us to infer characteristics of the population from a sample.
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13.1 Two Surprising Properties of Sampling
Infamous Case: The Literary Digest
The Literary Digest predicted defeat for Franklin D. Roosevelt in the 1936 presidential election. They selected their sample from a list of telephone numbers (telephones were a luxury during the Great Depression). Roosevelt’s supporters tended to be poor and were underrepresented in the sample.
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13.1 Two Surprising Properties of Sampling
This sample size is an almost infinitesimal portion of the population, yet the survey reveals attitudes of the entire population to within ± 3%
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13.1 Two Surprising Properties of Sampling
Simple Random Sample (SRS)
A sample of n items chosen by a method that has an equal chance of picking any sample of size n from the population.
Is the standard to which all other sampling methods are compared.
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13.1 Two Surprising Properties of Sampling
Simple Random Sample (SRS)
Sampling Frame: a list of items from which to select a random sample.
Systematic Sampling: method for selecting items from a sampling frame that follows a regular pattern (e.g., every 10th item).
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13.1 Two Surprising Properties of Sampling
Identifying the Sampling Frame
If there is no fixed population of outcomes, no sampling frame exists (e.g., output from a production process).
The list available may differ from the list desired (e.g., voter registration lists identify people who can vote, not those who will).
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13.2 VARIATION
Estimating Parameters
Parameter: a characteristic of the population (e.g., µ)
Statistic: an observed characteristic of a sample (e.g., )
Estimate: using a statistic to approximate a parameter
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y
13.2 VARIATION
Notation for Statistics and Parameters
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13.2 VARIATION
Sampling Variation
Is the variability in the value of a statistic from sample to sample.
The price we pay for working with a sample rather than the population.
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13.2 VARIATION
Sampling Variation in Sample Proportions
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4M Example 13.1: EXIT SURVEYS
Motivation
Why do customers leave a busy clothing store in the mall without making a purchase?
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4M Example 13.1: EXIT SURVEYS
Method
A survey is necessary. The owner decides to survey 50 weekend customers. The ideal sampling frame would list every customer who did not make a purchase over the weekend. Such a list does not exist.
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4M Example 13.1: EXIT SURVEYS
Mechanics
Interview every 10th customer who departs the store on the weekend. Based on typical customer flow, a sample of size 60 is expected. Ask customers why they didn’t make a purchase.
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4M Example 13.1: EXIT SURVEYS
Message
On the basis of the survey, the owner will be able to find out why shoppers are leaving without buying.
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13.3 ALTERNATIVE SAMPLING METHODS
Stratified Samples
Divide the sampling frame into homogeneous groups, called strata
Use simple random sample to select items from each strata
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13.3 ALTERNATIVE SAMPLING METHODS
Cluster Samples
Divide a geographic region into clusters
Randomly select clusters
Randomly choose items within selected clusters
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4M Example 13.2: ESTIMATING THE RISE OF PRICES
Motivation
What goes into determining the consumer price index (CPI), the official measure of inflation?
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4M Example 13.2: ESTIMATING THE RISE OF PRICES
Method
The Bureau of Labor Statistics (BLS) uses a survey to estimate inflation. The target population consists of the costs of every consumer transaction in urban areas during a specific month.
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4M Example 13.2: ESTIMATING THE RISE OF PRICES
Mechanics
The BLS has a list of urban areas and a list of people living in each, but does not have a list of every sales transaction. So the BLS divides items sold into 211 categories and estimates the change in price for each category in every area.
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4M Example 13.2: ESTIMATING THE RISE OF PRICES
Message
The urban consumer price index is an estimate of inflation base on a complex, clustered sample in selected metropolitan areas.
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13.3 ALTERNATIVE SAMPLING METHODS
Census
A comprehensive survey of the entire population.
Cost and time constraints generally prohibit carrying out a census; in some cases a census is not feasible.
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13.3 ALTERNATIVE SAMPLING METHODS
Voluntary Response
A sample consisting of individuals who volunteer when given the opportunity to participate in a survey.
These samples are biased toward those with strong opinions.
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13.3 ALTERNATIVE SAMPLING METHODS
Convenience Samples
A sampling method that selects individuals who are readily available.
Although easy to obtain, these samples are rarely representative.
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13.4 CHECKLIST FOR SURVEYS
Questions to Consider
What was the sampling frame? Is the sample a simple random sample? What is the rate of nonresponse? How was the question worded? Did the interviewer affect the results? Does survivor bias affect the survey?
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13.4 CHECKLIST FOR SURVEYS
How Wording of the Question Affects Results
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Best Practices
Randomize.
Plan carefully.
Match the sampling frame to the target population.
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Best Practices (Continued)
Keep focused.
Reduce the amount of nonresponse.
Pretest your survey.
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